Evolutionary optimization based on chaotic sequence in dynamic environments

Optimization issues are often defined statically, assuming constant environmental conditions.However, in many real-world scenarios, problem environments are dynamic and continuously changing.Thus we need optimization algorithms that could solves those issues in dynamic environments as well.Dynamic optimization problems are change(s) that may occur through the time.Such environments are characterized by uncertainty, temporal changes, and structural complexities, which makes the optimization process a significant challenge.In addressing these challenges, evolutionary algorithms have emerged as one of the most effective approaches for solving dynamic optimization problems (DOPs).Among these algorithms, the Imperialist Competitive Algorithm (ICA), designed based on swarm intelligence and competition among imperialist countries, has garnered considerable attention due to its capability in solving static optimization issues.In this research, Imperialist Competitive Algorithms, inspired by the historical and political processes of colonization and assimilation, have been known as one of the efficient evolutionary algorithms.These algorithms face numerous challenges when dealing with dynamic problems , including reduced population diversity, performance degradation in conditions of rapid environmental changes, and limitations in optimal convergence.These cases indicate the need to develop improved and more adaptable versions of these algorithms.Using concepts such as memory, population clustering, and repulsion mechanisms, this algorithm has been able to maintain population diversity at all stages while increasing the speed of convergence in the face of environmental changes.The key feature of the proposed algorithm is the use of memory to store previous optimal solutions, a clustering mechanism to manage population diversity, and repulsion to prevent unnecessary accumulation of solutions in specific regions.Nevertheless, ICA exhibits poor performance in dynamic environments because it lacks mechanisms to maintain diversity, quick adaptation to environmental changes, and new optima track.This study presents an improved version of ICA aimed at overcoming these limitations.The proposed algorithm incorporates a combination of a memory mechanism and a clustering strategy to enhance its adaptability to environmental changes and preserve diversity within the population.The memory mechanism stores information about previous optima and utilizes it under appropriate conditions to accelerate the optimization process.forclustering method is used for clustering.Clustering in the proposed method ensures that diversity is maintained for the population during the execution of the algorithm.In this study, our goal is to solve problems that change the environment in a global way.That means, the fitness of all points in the environment changes.By testing just one point in the environment and comparing the fitness obtained with its previously stored value, we can detect a change in the environment.On the other hand, the clustering strategy, particularly the k-means technique, to maintain maintain population diversity and prevents the convergence of solutions to specific regions.Together, these two components create a balance between exploration and exploitation, thereby improving the algorithm's performance in dynamic environments.To evaluate the performance of the proposed algorithm, the Moving Peaks Benchmark (MPB) was used as a standard metric.Due to its capability to simulate complex and diverse changes in dynamic environmentsparticularly in Branke's second scenario-MPB is one of the most recognized tools for assessing the performance of dynamic optimization algorithms.The proposed algorithm was evaluated alongside advanced algorithms such as FTmPSO (TMO), RAmQSO-s4, RmNAFSA-s4, TFTmPSO, RFTmPSO, mQSO10 (5+5q), FMSO, CellularPSO, Multi-SwarmPSO, mCPSO, AmQSO*, FTMPSO, almPSO, and CDEPSA.Experimental results demonstrated that the proposed algorithm outperformed other methods in areas such as convergence speed, adaptability to environmental changes, and population diversity preservation.A key feature of the proposed algorithm is its ability to retain identified optima even after environmental changes.Additionally, the use of the k-means clustering technique has ensured that the algorithm effectively avoids excessive focus on specific regions and maintains population diversity while facing complex environmental changes.Another advantage of this algorithm is its scalability in handling dynamic optimization issues with high dimensions and complexities.These findings indicate that the proposed algorithm is not only effective in laboratory settings but also suitable for real-world applications with fast and dynamic changes.

In recent years, there has been a growing interest in the study of particle swarm optimization (PSO) in dynamic environments. This paper presents a new PSO model, called PSO with composite particles (PSO-CP), to address dynamic optimization problems. PSO-CP partitions the swarm into a set of composite particles based on their similarity using a "worst first" principle. Inspired by the composite particle phenomenon in physics, the elementary members in each composite particle interact via a velocity-anisotropic reflection scheme to integrate valuable information for effectively and rapidly finding the promising optima in the search space. Each composite particle maintains the diversity by a scattering operator. In addition, an integral movement strategy is introduced to promote the swarm diversity. Experiments on a typical dynamic test benchmark problem provide a guideline for setting the involved parameters and show that PSO-CP is efficient in comparison with several state-of-the-art PSO algorithms for dynamic optimization problems.

This paper proposes to solve the dynamic optimization problem (DOP) by using an adaptive particle swarm optimization (APSO) algorithm with an variable relocation strategy (VRS). The VRS based APSO algorithm (APSO/VRS) has the following two advantages when solving DOP. Firstly, by using the APSO optimizing framework, the algorithm benefits from the fast optimization speed due to the adaptive parameter control. More importantly, the adaptive parameter and operator in APSO make the algorithm fast respond to the environment changes of DOP. Secondly, VRS was reported in the literature to help dynamic evolutionary algorithm (DEA) to relocate the individual position in promising region when environment changes. Therefore, the modified VRS used in APSO can collect historical information in the stability stage and use such information to guide the particle variable relocation in the change stage. We evaluated both APSO and APSO/VRS on several dynamic benchmark problems and compared with two state-of-the-art DEAs and DEA that also used the VRS. The results show that both APSO and APSO/VRS can obtain very competitive results on these problems, and APSO/VRS outperforms others on most of the test cases.

Several approaches have been developed into evolutionary algorithms to deal with dynamic optimization problems, of which memory and random immigrants are two major schemes. This paper investigates the application of a direct memory scheme for univariate marginal distribution algorithms (UMDAs), a class of evolutionary algorithms, for dynamic optimization problems. The interaction between memory and random immigrants for UMDAs in dynamic environments is also investigated. Experimental study shows that the memory scheme is efficient for UMDAs in dynamic environments and that the interactive effect between memory and random immigrants for UMDAs in dynamic environments depends on the dynamic environments.

The Evolutionary Algorithms (EA) are target of major studies regarding their use in dynamic optimization problems. This observation reflects the real importance of AE in real world applications. Many studies have been developed in order to have a better understand over the memory schemes. This work investigates the application of Multi-PBIL method on dynamic search spaces, using memory schemes. The Multi-PBIL is an optimization algorithm that belongs to the class of evolutionary algorithms. An adaptation is proposed to improve its adaptability in dynamic environments. In memory schemes, the probability models are stored in memory, along with the best samples created in a search space and they are used to reactivate old environments from the point when changes occur. Experimental studies based on a series of dynamic environments shows the efficiency of the memory scheme for the proposed method. This work presents also the relationship between the memory scheme and the multi-population in dynamic environments. Keywords: Estimation Distribution Algorithm, Dynamic Optimization Problem, Scheme Memory, Multi-PBIL, Evolutionary computation.

In this paper we propose a self adaptive cluster based Differential Evolution (DE) algorithm to solve the Dynamic Optimization Problems (DOPs). We have enhanced the classical DE to perform better in dynamic environments by a powerful clustering technique. During evolution, the information gained by the particles of different clusters is exchanged by a self adaptive strategy. The information exchange is done by re-clustering, and the cluster number is updated adaptively throughout the optimization process. To detect the environment change a test particle is used. Moreover, to adapt the population in new environment an External Archive is also used. The performance of SACDEEA is evaluated on GDBG benchmark problems and compared with other existing algorithms.KeywordsDifferential EvolutionDynamic Optimization Problem (DOP)Self adaptive clustering

A pareto-based evolutionary algorithm using decomposition and truncation for dynamic multi-objective optimization

Dynamic multiobjective optimization problem (DMOP) is a class of complex dynamic optimization problem (DOP), its widely exists in many real-world problems. Firstly, an core estimation of distribution model which used to approximately estimate the Pareto solution in the next environment is given, when a change in the environment is detected, the algorithm uses the collected information from the previous searching environments to predict the location of the Pareto solution in the next environment. Furthermore, a dynamic multiobjective optimization evolutionary algorithm with core estimation of distribution is proposed. The computer simulations are made on two dynamic multiobjective optimization problems, and the results indicate the proposed algorithm is effective.

Dynamic multi-objective optimisation problems have more than one objective with at least one objective that changes over time. Previous studies indicated that different knowledge sharing strategies increase the performance of the dynamic vector evaluated particle swarm optimisation (DVEPSO) algorithm in different dynamic environments. Therefore, this paper investigates the performance of the DVEPSO algorithm using heterogeneous particle swarm optimisation (HPSO) algorithms, where each particle uses a different knowledge sharing strategy. The goal of this study is to determine whether the use of HPSOs will improve the performance of DVEPSO by incorporating particles with different knowledge sharing strategies in a single DVEPSO algorithm. The results indicate that using HPSOs improves the performance of DVEPSO for dynamic multi-objective optimisation problems with a complex Pareto-optimal set and that the performance of heterogeneous DVEPSO compares favourably with that of DVEPSO.

Modified Differential Evolution with Locality induced Genetic Operators for dynamic optimization

Aiming to dynamic optimization problems (DOPs), this paper develops a novel general distributed multiple populations (DMP) framework for evolutionary algorithms (EAs). DMP employs six strategies designed in three levels (i.e., population-level, subpopulation-level, and individual-level) to deal with different kinds of DOPs. First, the population-level subpopulation division estimation strategy in initialization phase rationally divides the whole population into several subpopulations to explore distinct subareas of search space sufficiently. Then, during the steady evolutionary process, diversity preservation in individual-level and population-level accelerates the responsiveness of the whole population to a new landscape, while subpopulation-level self-learning of elitist individuals promotes the exploitation of promising areas. Moreover, in subpopulation-level, the archive quality assurance technique avoids repeat exploring the same peaks by storing the locations of different peaks with low redundancy. When landscape variation occurs, in population-level, historical information containing excellent evolutionary pattern is recorded to guide the population evolution better in the new environment. DMP framework is easy to implement in various EAs due to its well generality and independence about operators and parameters of the embedded algorithm. Four DMP-EAs are accomplished in this paper whose basic algorithms are particle swarm optimization (PSO) and differential evolution (DE) with different settings. The performance of the four proposed DMP-EAs is evaluated on all the widely used complex DOP benchmarks from CEC 2009. The testing results indicate that the DMP-EAs generally significantly outperform many state-of-the-art dynamic EAs (DEAs) on most of DOP benchmarks.

Solving online dynamic time-linkage problems under unreliable prediction

In the last years, there has been a large growth in the research of computational techniques inspired in nature. This area, named Bioinspired Computing, has provided biologically motivated solutions for several real world problems. Among Bioinspired Computing techniques, one can mention Artificial Neural Networks (ANN), Evolutionary Algorithms (EA), Artificial Immune Systems (AIS) and Ant Colony Optimization (ACO). ACO is a meta-heuristic based on the structure and behavior of ant colonies. It has been successfully applied to several optimization problems. Several real world optimization problems may change the configuration of its search space with time. These problems are known as dynamic optimization problems. This chapter presents the main concepts of ACO and show how it can be applied to solve real optimization problems on dynamic environments. As a case study, it will be illustrated how ACO can be applied to process scheduling problems. The chapter starts describing how real ants forage for food, environmental modifications related to this activity (for example, the blockage of a path) and the effects of these modifications in the colony. After, a brief review of previous works on Ant Colony Optimization is presented. For computer simulations, the activities of an ant colony may be modeled as a graph. After modeling the problem of foraging for food (as a graph), the goal (finding the shortest path at a given moment) is defined and the mechanism to solve the problem is presented. The need to model an on-line problem as a graph, the goal of finding the shortest path and the mechanisms adopted for solving the problem (an adapted version of the AntSystem) are detailed. Before ACO is applied to the process scheduling problem, the problem is analyzed and modeled using a graph representation. Next, simulation results obtained in a set of experiments are presented, which are validated by results obtained in a real implementation. Important issues related with the use of ACO for process scheduling, like parameter adjustments, are discussed. In the conclusion of this chapter, we point out a few future directions for ACO researches. The use of computational techniques inspired in nature has become very frequent in the last years. This area, named Bioinspired Computing, provides efficient biologically motivated

Dynamic optimization problems have gained significant attention in evolutionary computation as evolutionary algorithms (EAs) can easily adapt to changing environments. We show that EAs can solve the graph coloring problem for bipartite graphs more efficiently by using dynamic optimization. In our approach the graph instance is given incrementally such that the EA can reoptimize its coloring when a new edge introduces a conflict. We show that, when edges are inserted in a way that preserves graph connectivity, Randomized Local Search (RLS) efficiently finds a proper 2-coloring for all bipartite graphs. This includes graphs for which RLS and other EAs need exponential expected time in a static optimization scenario. We investigate different ways of building up the graph by popular graph traversals such as breadth-first-search and depth-first-search and analyse the resulting runtime behavior. We further show that offspring populations (e. g. a (1+$\lambda$) RLS) lead to an exponential speedup in $\lambda$. Finally, an island model using 3 islands succeeds in an optimal time of $\Theta(m)$ on every $m$-edge bipartite graph, outperforming offspring populations. This is the first example where an island model guarantees a speedup that is not bounded in the number of islands.

When facing dynamic optimization problems the goal is no longer to find the extrema, but to track their progression through the space as closely as possible. Over these kind of over changing, complex and ubiquitous real-world problems, the explorative-exploitive subtle counterbalance character of our current state-of-the-art search algorithms should be biased towards an increased explorative behavior. While counterproductive in classic problems, the main and obvious reason of using it in severe dynamic problems is simple: while we engage ourselves in exploiting the extrema, the extrema moves elsewhere. In order to tackle this subtle compromise, we propose a novel algorithm for optimization in dynamic binary landscapes, stressing the role of negative feedback mechanisms. The Binary Ant Algorithm (BAA) mimics some aspects of social insects' behavior. Like Ant Colony Optimization (ACO), BAA acts by building pheromone maps over a graph of possible trails representing pseudo-solutions of increasing quality to a specific optimization problem. Main differences rely on the way this search space is represented and provided to the colony in order to explore/exploit it, while and more important, we enrol in providing strong evaporation to the problem-habitat. By a process of pheromone reinforcement and evaporation the artificial insect's trails over the graph converge to regions near the ideal solution of the optimization problem. Over each generation, positive feedbacks made available by pheromone reinforcement consolidate the best solutions found so far, while enhanced negative feedbacks given by the evaporation mechanism provided the system with population diversity and fast self-adaptive characteristics, allowing BAA to be particularly suitable for severe complex dynamic optimization problems. Experiments made with some well known test functions frequently used in the Evolutionary Algorithms' research field illustrate the efficiency of the proposed method. BAA was also compared with other algorithms, proving to be more able to track fast moving extrema on several test problems.